Análise Taxa de Desemprego

raiz_unit(serie_desemprego)
## $ADF
## 
##  Augmented Dickey-Fuller Test
## 
## data:  ts
## Dickey-Fuller = -2.0429, Lag order = 6, p-value = 0.5579
## alternative hypothesis: stationary
## 
## 
## $PP
## 
##  Phillips-Perron Unit Root Test
## 
## data:  ts
## Dickey-Fuller Z(alpha) = -2.1946, Truncation lag parameter = 5, p-value
## = 0.963
## alternative hypothesis: stationary
## 
## 
## $KPSSL
## 
##  KPSS Test for Level Stationarity
## 
## data:  ts
## KPSS Level = 2.6349, Truncation lag parameter = 5, p-value = 0.01
## 
## 
## $Tabela
##                      Testes            H0 p_valor Conclusao
## 1   Augmented Dickey-Fuller     Tendencia  0.5579 Tendencia
## 2 Phillips-Perron Unit Root     Tendencia  0.9630 Tendencia
## 3       KPSS Test for Level NAO tendencia  0.0100 Tendencia
tend_determ(serie_desemprego)
## $CS
## 
##  Cox Stuart test
## 
## data:  ts
## statistic = 25, n = 133, p-value = 1.718e-13
## alternative hypothesis: non randomness
## 
## 
## $CeST
## 
##  Cox and Stuart Trend test
## 
## data:  ts
## z = 9.4868, n = 270, p-value < 2.2e-16
## alternative hypothesis: monotonic trend
## 
## 
## $MannKT
## 
##  Mann-Kendall trend test
## 
## data:  ts
## z = -12.049, n = 270, p-value < 2.2e-16
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
## -1.786200e+04  2.197416e+06 -4.965964e-01 
## 
## 
## $MannK
## tau = -0.497, 2-sided pvalue =< 2.22e-16
## 
## $KPSST
## 
##  KPSS Test for Trend Stationarity
## 
## data:  ts
## KPSS Trend = 0.83108, Truncation lag parameter = 5, p-value = 0.01
## 
## 
## $Tabela
##                 Testes            H0 p_valor Conclusao
## 1           Cox Stuart NAO tendencia    0.00 Tendencia
## 2 Cox and Stuart Trend NAO tendencia    0.00 Tendencia
## 3   Mann-Kendall Trend NAO tendencia    0.00 Tendencia
## 4         Mann-Kendall NAO tendencia    0.00 Tendencia
## 5  KPSS Test for Trend NAO tendencia    0.01 Tendencia
sazonalidade(serie_desemprego)
## $KrusW
## Test used:  Kruskall Wallis 
##  
## Test statistic:  0.21 
## P-value:  1
## 
## $Fried
## Test used:  Friedman rank 
##  
## Test statistic:  22.94 
## P-value:  0.01805006
## 
## $Tabela
##            Testes          H0 p_valor   Conclusao
## 1 Kruskall Wallis NAO Sazonal  1.0000 NAO Sazonal
## 2   Friedman rank NAO Sazonal  0.0181     Sazonal
serie_desemprego_part <- ts_split(serie_desemprego, sample.out = 12)
serie_desemprego_train <- serie_desemprego_part$train
serie_desemprego_test <- serie_desemprego_part$test


modelo1 <- auto.arima(serie_desemprego_train)

summary(modelo1)
## Series: serie_desemprego_train 
## ARIMA(1,2,1)(0,0,2)[12] 
## 
## Coefficients:
##           ar1      ma1     sma1     sma2
##       -0.3353  -0.4303  -0.1283  -0.1507
## s.e.   0.0941   0.0940   0.0638   0.0619
## 
## sigma^2 = 4.064e-07:  log likelihood = 1521.71
## AIC=-3033.42   AICc=-3033.18   BIC=-3015.69
## 
## Training set error measures:
##                         ME         RMSE          MAE          MPE      MAPE
## Training set -1.551009e-05 0.0006300452 0.0004884268 -0.008591897 0.6315899
##                    MASE        ACF1
## Training set 0.07268784 0.002654839
modelo1_fc <- forecast::forecast(modelo1, h = 12)

coeftest(modelo1)
## 
## z test of coefficients:
## 
##       Estimate Std. Error z value  Pr(>|z|)    
## ar1  -0.335297   0.094064 -3.5646 0.0003645 ***
## ma1  -0.430321   0.093992 -4.5783 4.688e-06 ***
## sma1 -0.128297   0.063773 -2.0118 0.0442456 *  
## sma2 -0.150657   0.061931 -2.4327 0.0149877 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
forecast::accuracy(modelo1_fc, serie_desemprego_test)[,c(1:3, 5)]
##                         ME         RMSE          MAE      MAPE
## Training set -1.551009e-05 0.0006300452 0.0004884268 0.6315899
## Test set      2.258501e-03 0.0025234201 0.0022585006 5.1714145
test_forecast(actual = serie_desemprego,
              forecast.obj = modelo1_fc,
              test = serie_desemprego_test)